Confinement-induced resonances for the creation of quasi-one-dimensional ultra cold gases of alkali--alkaline-earth dimers

We theoretically investigate the role of confinement-induced resonances (CIRs) in low-dimensional ultracold atomic mixtures for the formation of weakly bound dimers. To this end, we examine the scattering properties of a binary atomic mixture confined by a quasi-one-dimensional (quasi-1D) potential. In this regime, the interspecies two-body interaction is modeled as an effective 1D zero-range pseudopotential, with a coupling strength $g_\mathrm{1D}$ derived as a function of the three-dimensional scattering length $a$. This framework enables the study of CIRs in harmonically confined systems, with particular attention to the case of mismatched transverse trapping frequencies for the two atomic species. Finally, we consider the Bose-Fermi mixture of $^{87}$Rb and $^{87}$Sr, and identify values of the experimentally accessible parameters for which CIRs can be exploited to create weakly bound molecules.